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Module « scipy.stats »

Fonction ranksums - module scipy.stats

Signature de la fonction ranksums

def ranksums(x, y, alternative='two-sided', *, axis=0, nan_policy='propagate', keepdims=False) 

Description

help(scipy.stats.ranksums)

    


Compute the Wilcoxon rank-sum statistic for two samples.

The Wilcoxon rank-sum test tests the null hypothesis that two sets
of measurements are drawn from the same distribution.  The alternative
hypothesis is that values in one sample are more likely to be
larger than the values in the other sample.

This test should be used to compare two samples from continuous
distributions.  It does not handle ties between measurements
in x and y.  For tie-handling and an optional continuity correction
see `scipy.stats.mannwhitneyu`.

Parameters
----------
x,y : array_like
    The data from the two samples.
alternative : {'two-sided', 'less', 'greater'}, optional
    Defines the alternative hypothesis. Default is 'two-sided'.
    The following options are available:
    
    * 'two-sided': one of the distributions (underlying `x` or `y`) is
      stochastically greater than the other.
    * 'less': the distribution underlying `x` is stochastically less
      than the distribution underlying `y`.
    * 'greater': the distribution underlying `x` is stochastically greater
      than the distribution underlying `y`.
    
    .. versionadded:: 1.7.0
axis : int or None, default: 0
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.
    
    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
statistic : float
    The test statistic under the large-sample approximation that the
    rank sum statistic is normally distributed.
pvalue : float
    The p-value of the test.

Notes
-----

Beginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
code) are converted to ``np.ndarray`` before the calculation is performed. In
this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
masked array with ``mask=False``.

References
----------
.. [1] https://en.wikipedia.org/wiki/Wilcoxon_rank-sum_test

Examples
--------
We can test the hypothesis that two independent unequal-sized samples are
drawn from the same distribution with computing the Wilcoxon rank-sum
statistic.

>>> import numpy as np
>>> from scipy.stats import ranksums
>>> rng = np.random.default_rng()
>>> sample1 = rng.uniform(-1, 1, 200)
>>> sample2 = rng.uniform(-0.5, 1.5, 300) # a shifted distribution
>>> ranksums(sample1, sample2)
RanksumsResult(statistic=-7.887059,
               pvalue=3.09390448e-15) # may vary
>>> ranksums(sample1, sample2, alternative='less')
RanksumsResult(statistic=-7.750585297581713,
               pvalue=4.573497606342543e-15) # may vary
>>> ranksums(sample1, sample2, alternative='greater')
RanksumsResult(statistic=-7.750585297581713,
               pvalue=0.9999999999999954) # may vary

The p-value of less than ``0.05`` indicates that this test rejects the
hypothesis at the 5% significance level.

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